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Improved Fan subequation method; bifurcation method; generalized KdV equation; soliton solution; kink solution; periodic solution.

In this paper, by using a transformation and an application of Fan subequation, we study a class of generalized Korteweg–de Vries (KdV) equation with generalized evolution. As a result, more types of exact solutions to the generalized KdV equation with generalized evolution are obtained, which include more general single-hump solitons, multihump solitons, kink solutions and Jacobian elliptic function solutions with double periods.

Yongan Xie¹ Shengqiang Tang¹ Dahe Feng¹

1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, People’s Republic of China

Published

April 2012

Manuscript received

13 July 2011

Manuscript revised

11 November 2011

Accepted

8 December 2011